Numerical Methods

in mathematics, methods of approximate solution of mathematical problems through the performance of a finite number of elementary operations on numbers.

The elementary operations used are arithmetic operations, generally carried out approximately, and subsidiary operations, such as recording intermediate results and extracting information from tables. Numbers are expressed by a limited set of digits in some positional numeration system, for example, the decimal or binary system. The number line is thus replaced by a discrete system of numbers, sometimes called a net. A function of a continuous variable accordingly is replaced by a table of the function’s values in this discrete system of numbers (seeMATHEMATICALTABLE). Operations of analysis that act on continuous functions are replaced by algebraic operations on the function’s values in the table. Numerical methods reduce the solution of mathematical problems to computations that can be performed manually or by means of calculating machines. The development of new numerical methods and their use in computers have led to the rise of computer mathematics.